MPSI - Week 14

The point-biserial correlation is used to measure the relationship between two variables when:

• Both variables consist of regular, numerical scores

• One variable consists of regular, numerical scores and the other has only two values

• Both variables are dichotomous

• Both variables are continuous and normally distributed

Answer explanation

The Point-Biserial Correlation

The point-biserial correlation is used to measure the relationship between two variables in situations in which one variable consists of regular, numerical scores, but the second variable has only two values.

A variable with only two values is called a dichotomous variable or a binomial variable.

Some examples of dichotomous variables are:

1. male vs. female

2. college graduate vs. not a college graduate

3. first-born child vs. later-born child

In the context of the point-biserial correlation, a variable with only two values is ....

• Bivariate

• Continuous

• Ordinal

• Dichotomous

Answer explanation

The Point-Biserial Correlation

The point-biserial correlation is used to measure the relationship between two variables in situations in which one variable consists of regular, numerical scores, but the second variable has only two values.

A variable with only two values is called a dichotomous variable or a binomial variable.

Some examples of dichotomous variables are:

1. male vs. female

2. college graduate vs. not a college graduate

3. first-born child vs. later-born child

Which of the following situations would be suitable for applying the point-biserial correlation?

• Comparing the relationship between income levels and job satisfaction

• Examining the correlation between height and weight

• Investigating the association between gender and voting preference

• Measure the relationship between age and education level

Answer explanation

The Point-Biserial Correlation

The point-biserial correlation is used to measure the relationship between two variables in situations in which one variable consists of regular, numerical scores, but the second variable has only two values.

A variable with only two values is called a dichotomous variable or a binomial variable.

Some examples of dichotomous variables are:

1. male vs. female

2. college graduate vs. not a college graduate

3. first-born child vs. later-born child

What did the research by Zhong, Bohns, & Gino (2010) reveal about people's behavior in different lighting conditions?

• People are more likely to show dishonest behavior in a well-lit environment.

• People are more likely to show self-interested behavior in darkness.

• People are more likely to show dishonest and self-interested behaviors in darkness.

• People's behavior remains consistent regardless of lighting conditions.

Answer explanation

The Point-Biserial Correlation

Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010).

In one research, participants were given a set of 20 puzzles and were paid $1 for each one solved in a 5-minute period. The participants reported their own performance and there was no obvious method for checking their honesty. Thus, the task provided a clear opportunity to cheat and receive undeserved money. One group of participants was tested in a room with dimmed lighting and a second group was tested in a well-lit room.

Which statistical measure is often considered to evaluate similar aspects as the independent-measures hypothesis test?

• Pearson correlation coefficient

• Spearman rank correlation coefficient

• Point-biserial correlation coefficient

• Phi coefficient

Answer explanation

The Point-Biserial Correlation

In some respects, the point-biserial correlation and the independent-measures hypothesis test are evaluating the same thing.

Which of the following best describes the relationship between the Point-Biserial Correlation (r) and the t value in hypothesis testing?

• The t value measures the effect size, while r measures statistical significance.

• The t value measures statistical significance, while r measures the effect size.

• Both the t value and r measure statistical significance.

• Both the t value and r measure the effect size.

Answer explanation

The Point-Biserial Correlation and t

The outcome of the hypothesis test and the value of r^2 are often reported together. The t value measures statistical significance and r^2 measures the effect size. In fact, either can be calculated from the other by the equations:

Which of the following statements best describes the relationship between the Point-Biserial Correlation (r) and the t statistic?

• They are entirely independent of each other.

• The t statistic is solely determined by the size of the correlation (r).

• The t statistic is influenced by both the size of the correlation (r) and the sample size.

• The Point-Biserial Correlation (r) and the t statistic measure the same thing.

Answer explanation

The Point-Biserial Correlation and t

r^2 is determined entirely by the size of the correlation, whereas t is influenced by the size of the correlation and the size of the sample. Although t and r are related, they are measuring different things.

What factors influence the t statistic?

• Neither the size of the correlation (r) nor the size of the sample

• Only the size of the sample

• Both the size of the correlation (r) and the size of the sample

• Only the size of the correlation (r)

Answer explanation

The Point-Biserial Correlation and t

r^2 is determined entirely by the size of the correlation, whereas t is influenced by the size of the correlation and the size of the sample. Although t and r are related, they are measuring different things.

What is the Phi-Coefficient used to measure?

• Correlation between two continuous variables

• Correlation between two dichotomous variables

• Correlation between a continuous variable and a dichotomous variable

• Correlation between multiple categorical variables

Answer explanation

The Phi-Coefficient Φ

When both variables (X and Y) measured for each individual are dichotomous, the correlation between the two variables is called the phi-coefficient.

To compute phi (Φ):

Convert each of the dichotomous variables to numerical values by assigning a 0 to one category and a 1 to the other category for each of the variables. Use the regular Pearson formula with the converted scores.

How are dichotomous variables converted to numerical values for computing the Phi-Coefficient?

• By assigning 0 to both categories

• By assigning 0 to one category and 1 to the other category for each variable

• By assigning 1 to both categories

• By assigning random numerical values to each category

Answer explanation

The Phi-Coefficient Φ

When both variables (X and Y) measured for each individual are dichotomous, the correlation between the two variables is called the phi-coefficient.

To compute phi (Φ):

Convert each of the dichotomous variables to numerical values by assigning a 0 to one category and a 1 to the other category for each of the variables. Use the regular Pearson formula with the converted scores.